This is a bug in 10.8.
To be more precise: after using AirPlay Mirroring in one account, one needs to log out that account before one can use Mirroring in another account on that same Mac. The same applies if you happen to use Mirroring in the guest account first, and then leave that account logged in and try to use Mirroring in some regular account.
Also, any text you might recognize is not from the current screen of the other account, but from the last Mirroring session of that account. The current screen might already not show that text anymore.
(It's fine to log in again right after logging out; apparently some cleaning up is done when logging out. I've reported it, but unfortunately used Apple's feedback form, rather than the developer Bug Reporting. Hence, I cannot see the status of my report. I will delete all this if it's fixed in some future version.)